Monday, March 23, 2009

(As part of Rabett Run's Gerlich and Tscheuschner project, Eli has started drafting parts of a response, which we will gift wrap in Bozo paper and send to some unsuspecting journal, but certainly arXiv. This second part comes from Chris Colose. The Editorial Board expresses its thanks=:> [Rabett Run has an exceedingly small Editorial Board] Suggestions for changes and additions are welcome. I think this makes much the same point as Joel Schor's model, with the advantage that it is somewhat clearer how it fits in with the sun/earth system. It might be substituted for it, after which we could place the section about the rotating earth and average temperatures. - Eli)

Request: I need a solar spectrum taken from space that extends to the IR preferably 10-4 microns, again, preferably in digital format. Resolution need not be high

UPDATE: Minor corrections 11:30 PM 3/24

All objects with a temperature emit energy according to the Planck radiation law. It has been shown above how objects of differing temperatures placed near each other must continue to radiate energy towards each other, and so cooler bodies must emit energy toward hotter ones. Gerlich and Tscheuschner (2009) believe that this state of affair represents a contradiction to thermodynamics. Above, we have looked at perhaps the simplest example that shows them to be wrong. The same logic can be applied to a simplified atmosphere represented by a number of blackbody layers which radiate energy in all directions.

This is not too far from how real radiative transfer codes work, with the caveat that here only two "gray" layers are considered. For simplicity, we assume that the atmospheric layers are opaque to infrared radiation, absorbing all terrestrial IR radiation, and emitting like a blackbody at their temperatures. This simplified atmosphere is also fully transparent to incoming solar radiation. An atmosphere with large infrared optical depth can be approximated with two layers centered at 0.5 and 2 km altitude (Goody and Walker 1972).

In this model, the amount of radiation absorbed on the surface equals the solar flux in W/m2 at the top of the atmosphere, S, less that reflected back to space, the albedo, α, divided by 4, which accounts for the fact that the earth is spherical (for details see, for example, Insert Ref). The top layer (Layer 2) emits IR radiation that matches the solar radiation absorbed by the surface. In this simplified model, the temperature of the second layer is the effective temperature of the planet as observed from space. Below, we will consider a more complicated model for a rotating planet, again, reaching different conclusions than Gerlich and Tscheuschner, and again, will point out why their conclusions are in error. At equilibrium, each level must absorb and emit the same amount of radiation. This leads to three simple equations

(1) At the surface: S(1-α)/4 + σT14 = σTsur4

(2) At Layer 1: σT24 + σTsur4 = 2 σT14

(3) At Layer 2: σT14 = 2 σT24

Starting with the observed solar flux at the top of the atmosphere, 1364 W/m2, we can solve for

T2 = 255 K
T1 = 303 K
Tsur = 335 K

Because Tsur in Table 1 is too high, the assumption that only radiation governs the atmospheric thermal equilibrium has to be modified. In reality, evaporation of water from the surface and its condensation in the atmosphere, the latent and sensible heat fluxes, remove substantial amounts of energy from the surface. In the global, annual mean these terms equate to roughly 100 W/m2 of energy removal from the surface and put in the atmosphere (Trenberth et al., 2009). Convection also plays a role

With or without considering convection or latent heats associated with the condensation of water vapor, the clear effect of the atmosphere is to make the surface temperature much higher than the effective temperature at which it radiates to space. These layers introduce another aspect to the supply of energy at the surface, which now is not only heated by the sun, but also by the downward emission of terrestrial radiation from the atmosphere. This term is larger than the incident solar radiation at the surface by a factor of roughly two in the global mean. Most of this terrestrial radiation originates in the lower atmosphere where water vapor is very abundant. As shown by the spectrum below the down welling radiation has been measured directly, again contrary to the assertions of Ref. 1. In this spectrum, taken at the pole, one sees the influence of water vapor as the sharp lines, mostly at the left, low frequency end, CO2 between 600 and 800 cm-1, and ozone at about 1100 cm-1.

Under typical conditions, most of the outgoing longwave radiation originates in the troposphere at altitudes much colder than the surface. Again, this has been measured directly from space

When more greenhouse gases are added to the atmosphere, energy can only radiate from higher altitudes where the inflow of energy then becomes greater than the outgoing longwave flux at the top of the atmosphere. The greenhouse warming is thus (Hansen et al. 1981),

(4) Tsur = Teff + ΓH

where Gamma (Γ) is the lapse rate and H is the height above the surface. In this way, the increased atmospheric CO2 restricts the outflow of thermal radiation, and the planetary surface temperature can only rise. This situation is illustrated in Figure 2.

Gerlich and Tscheuschner (2009) are correct to conclude that this greenhouse mechanism does not act in the way real greenhouse acts, whereby convection is restricted, however this is a strawman, a strawman that occupies over 20 pages in Ref 1. No serious explanation of the greenhouse effect neglect the role of radiation and how it is suppressed with increased infrared opacity. On Earth, absorption and re-radiation of infrared energy is the reason why the actual surface temperature is much higher than that of the effective temperature. Although scattering of infrared light is not a significant term for the Earth's atmosphere, it can matter in other planetary cases such as Venus or past conditions on Mars (e.g., Forget and Pierrehumbert 1997).

Gerlich and Tscheuschner (2009) conclude that most of the infrared absorption in the atmosphere is due to water vapor, and that because CO2 only absorbs in a small part of the total infrared spectrum, raising its partial pressure will have little effect. This claim is very misleading and especially if one does not have a working knowledge of the infrared spectrum of both molecules. There is no physical meaning in comparing CO2’s absorption to the “total infrared spectrum” since the boundaries between infrared and other areas of the electromagnetic spectrum are arbitrary. What is important is that CO2 absorbs very strongly near the peak emission at Earth-like temperatures, and renders the atmosphere completely opaque between 14 and 16 microns, and partially absorbing still some distance from those edges (Petty 2006). As CO2 builds up in the atmosphere, there will still be significant absorption away from the line center, in the wings of the absorption area. This is an area of the spectrum in which water vapor is a weak absorber, and because the atmosphere is so dry at the colder, higher altitudes where radiative balance is set, CO2 is not swamped by water vapor’s greenhouse effect.

Of the 33 K greenhouse effect, roughly 50% of the infrared opacity is due to water vapor, 25% due to clouds, 20% from CO2, and the remaining 5% from other non-condensable greenhouse gases such as ozone, methane, and nitrous oxide (Kiehl and Trenberth 1997). Although this often leads to popular statements such as “water vapor is the most important greenhouse gas,” a more complete picture is that those gases which do not precipitate from the atmosphere under Earth’s current temperature regime (including CO2, ozone, methane) provide the supporting framework for which the condensable substances (water vapor and clouds) can act. As such, if CO2 and the other non-condensable gases were to be removed from the atmosphere, the colder temperature would then result in a substantial reduction of water vapor and clouds, and a collapse of the terrestrial greenhouse effect. On the other hand, as one makes the planet warmer by adding CO2 to the atmosphere, the saturation pressure for water will increase and result in a substantial positive feedback to amplify warming (e.g., Held and Soden 2000).

Not IR from the sky... but relevant to this project is a reference to an early direct measurement of the IR backradiation from the atmosphere to the surface, which G&T believe would conflict with the second law.

See: Stern, S.C., and F. Schwartzmann, 1954: An Infrared Detector For Measurement Of The Back Radiation From The Sky. J. Atmos. Sci., 11, 121–129. Available online.

Measurements in the paper are given in cal/cm^2/min, which can be converted to W/m^2 by multiplying by 697. Measured values (Frederick, Maryland) converted to W/m^2 in the daytime ranged from 314 to 405 W/m^2; and at night from 206 to 312 W/m^2. That's substantially more than the average input to the surface from the Sun.

In another post here, proposed values were given as percentages of the TOA insolation (342 W/m^2). The backradiation quoted there was 88%, which corresponds to about 300 W/m^2.

Anonymous - obviously this is hardly original research - Rabett is attempting to rephrase exceedingly well-established science to address the specific misconceptions of Gerlich and Tscheuschner. Sometimes you have to tell people something half a dozen different ways before they "get it". And sometimes they never do, but it's worth the attempt anyway.

That last "anonymous" was me, by the way (from my iPhone, having forgotten my password).

By the way, convection == sensible heat flow, as far as I'm aware. Latent heat is the energy associated with water vapor (the phase change energy from liquid to gas and back again).

On yet another subject from G&T, I've been thinking about the "greenhouse" analogy a bit, and I think there are several real ironies in their dismissive treatment of it.

Literal greenhouses work by blocking convection, so they centrally require a surrounding atmosphere, which is ignored by G&T in most of the rest of the paper. A greenhouse on the moon would not make the ground any warmer during day time, nor would it make it cool any slower during the night.

The greenhouse on Earth warms faster during the daytime because it restricts convective and latent heat transfer, so essentially all exchange with the outside world has to be by radiation. This allows the surface to come closer to the G&T ideal local instantaneous radiative balance number T_phys. Except there is *more* incoming radiation to the surface than just the incoming solar - because of back-radiation.

The back-radiation from the rest of the atmosphere particularly plays its role at night, allowing a greenhouse to stay much warmer than the dark-side-of-the-Moon temperatures you would reach without it (though the heat stored through water in the greenhouse makes the heat capacity effectively much higher than you'd get on the Moon, also).

In a sense, a greenhouse works because it grabs pretty much all the incoming solar in its little area during the day time, and then relies on the surrounding region to capture lots more solar energy to keep it even warmer during the day, and particularly warm at night.

About ten years ago, Eli was waiting for a flight to a small place with a large conference, with a number of folk very important in the atmospheric chemistry community.

Over beverages of choice the bunny asked why they didn't speak up when Dick Lindzen committed crap. The answer was, well, he is a bit nuts, but it harms no one, and it is sort of what he does. No harm.

normally I'd agree with you. But the fact they got this gibberish past "review" in the physics journal they did is very worrysome, and that fact also makes it a citable source, and an authoritative source for those who don't have the background to tell the difference.

I'm not sure this is a waste of time on the basis that nothing here is original. Any place that this "rabett rebuttal" is published isn't necessarily a place for original research anyway (we're talking ArXiv, not GRL or Nature here). It would be worthwhile to have a response at least exist that can collect these thoughts on G&T into one document.

The WMO/WRDC Wehrli Air Mass Zero (AM 0) solar spectral irradiance curve has often been cited and used as the extraterrestrial solar spectal irradiance distribution. This spectral distribution was constructed in 1985, based on the following references:

Chris,Just some minor points about the spectra you've now included. The second one isn't from space, as the text says, but from 20km altitude. And it's worth noting that the two are, I believe, simultaneous at the same location.

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Eli Rabett

Eli Rabett, a not quite failed professorial techno-bunny who finally handed in the keys and retired from his wanna be research university. The students continue to be naive but great people and the administrators continue to vary day-to-day between homicidal and delusional without Eli's help. Eli notices from recent political developments that this behavior is not limited to administrators. His colleagues retain their curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they, or at least some of them occasionally heeded his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.